Exponential Function Models Worksheet With Answers Page 7
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7Math 117 Lecture 9 notes page 7
The amount g (in trillions of cubic feet) of natural gas consumed in the United States from 1940 to
1970 can be modeled by
t
G = 2.9(1.07)
where t is the number of years since 1940.
a)
Identify the initial amount, the growth factor, and the annual percent increase.
b)
Estimate the natural gas consumption in 1955.
The student enrollment E of a high school was 1240 in 1990 and increased by 15% per year until 1996.
Which exponential growth model shows the school's student enrollment in terms of t, the number of
years since 1990?
t
a)
E = 15(1240)
t
b)
E = 1240(1.15)
t
c)
E = 1240(15)
t
d)
E = 0.15(1240)
t
e)
E = 1.15(1240)
Practice problems:
1)
In 1965 the federal debt of the United States was $322.3 billion. During the
next 30 years, the debt increased by about 10.2% each year.
a)
Write a model giving the amount D (in billions of dollars) of debt t years
after 1965.
b)
About how much was the federal debt in 1980?
c)
Estimate the year when the federal debt was $2,120 billion.
2)
You deposit $2500 in a bank that pays 4% interest compounded annually. Use the process
below and a graphing calculator to determine the balance of your account each year.
a)
Enter the initial deposit, 2500, into the calculator. Then enter the formula ANS + ANS
X 0.04 to find the balance after one year.
b)
What is the balance after five years? (press Enter five times)
c)
How would you enter the formula in part (a) if the interest is compounded quarterly?
What would you have to do to find the balance after one year?
d)
Find the balance after 5 years if the interest is compounded quarterly. Compare this
result with your answer to part (b).
Homework #9 is the handout “Exponential Problems.” Answers are on the course website.
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